THE SPACE DENSITY OF GALAXY PEAKS AND THE LINEAR MATTER POWER SPECTRUM

One way of recovering information about the initial conditions of the universe is by measuring features of the cosmological density field th at are preserved during gravitational evolution and galaxy formation. In this paper we study the total number density of peaks in a (galaxy) point distribution smoothed with a filter, evaluating its usefulness as a means of inferring the shape of the initial (matter) power spectr um. We find that in numerical simulations that start from Gaussian ini tial conditions, the peak density follows well that predicted by the t heory of Gaussian density fields, even on scales where the clustering is mildly nonlinear. For smaller filter scales, r less than or similar to 4-6 h(-1) Mpc, we see evidence of merging as the peak density decr eases with time. On larger scales, the peak density is independent of time. One might also expect it to be fairly robust with respect to var iations in biasing, i.e., the way galaxies trace mass fluctuations. We find that this is the case when we apply various biasing prescription s to the matter distribution in simulations. If the initial conditions are Gaussian, it is possible to use the peak density measured from th e evolved held to reconstruct the shape of the initial power spectrum. We describe a stable method for doing this and apply it to several bi ased and unbiased nonlinear simulations. We are able to recover the sl ope of the linear matter power spectrum on scales k less than or simil ar to 0.4 h(-1) Mpc(-1). The reconstruction has the advantage of being independent of the cosmological parameters (Omega, Lambda, and H-0) a nd of the clustering normalization (sigma(g)). The peak density and re constructed power spectrum slope therefore promise to be powerful disc riminators between popular cosmological scenarios.